The point isn’t that the average investor in a given year will perform at the market average (this is what I think you are referring to by the tautological claim). The point is that over time the correlation between winners (retail or professional) one time period to the next is essentially zero.
My main point was that the quote you were "fixing":
> It turns out that the average person is just not very good at picking stocks
Is accurate, and not in need of correction.
As a sibling comment pointed out, the average for professionals is higher: by almost exactly what they cost, as it turns out. For various ergodic reasons, that means that an investor without personal alpha should stick with index funds.